Finite Group Databasebeta

← #24996815

Subgroups — #24996815

Order 11008.

872 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 872 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583038C211yesmaximal, characteristic
2#19140340C211yesmaximal, characteristic
3C2×#14582818C211yesmaximal, characteristic, complemented
4C2×#14582634C211yesmaximal, characteristic
5C2×#14582624C211yesmaximal, characteristic, complemented
6#19132473C211yesmaximal, characteristic, complemented
7C43×#1787C211yesmaximal, characteristic, complemented
8C22×#10621884—21no—
9C2×#13063309—21no—
10C2×#13063299C2211yescharacteristic
11C22×Dic43⋊C4—21no—
12C22×Dic43⋊C4C2211yescharacteristic
13#14583038—22no—
14#14583038—22no—
15C2×#13063249—21no—
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17#14582831—21no—
18#14582821—22no—
19#14582818—22no—
20#14582818—22no—
21#14582817—21no—
22#14582776—21no—
23C2×C43⋊#95—21no—
24C2×C43⋊#95C2211yescharacteristic
25#14582634—22no—
26#14582624—22no—
27C23×Q8×C43C2211yescharacteristic
28C2×#103×C43—22no—
29C2×C22⋊C8×C43C2211yescharacteristic
30C43×#380C2211yescharacteristic
31C22×D172D411yescharacteristic
32C22×C22⋊D43—21no—
33C23×Dic43—21no—
34C23×Dic43D411yescharacteristic
35C23×Dic43D411yescharacteristic
36C2×#10621884—24no—
37C2×#10621884—44no—
38C22×C43⋊C8—21no—
39#13063309—42no—
40#13063309—42no—
41#13063299—21no—
42#13063299—21no—
43#13063299—21no—
44#13063299—21no—
45C2×C4⋊Dic43—22no—
46C2×C4⋊Dic43D411yescharacteristic
47C2×Dic43⋊C4—24no—
48C2×Dic43⋊C4—21no—
49C2×Dic43⋊C4—21no—
50C2×Dic43⋊C4—21no—
51C2×Dic43⋊C4—21no—
52C2×Dic43⋊C4—21no—
53C2×Dic43⋊C4—21no—
54C2×Dic43⋊C4—44no—
55C2×(C2×D43)⋊C4—22no—
56C2×(C2×D43)⋊C4—21no—
57C2×(C2×D43)⋊C4—22no—
58#13063249—24no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)D412yes—
61C43⋊#95—24no—
62C43⋊#95—22no—
63C43⋊#95—21no—
64C43⋊#95D412yes—
65C22×Q8×C43—21no—
66C22×Q8×C43—21no—
67C22×Q8×C43—21no—
68C22×Q8×C43—21no—
69C22×Q8×C43—21no—
70C22×Q8×C43—44no—
71C22×Q8×C43D412yes—
72C23×C4×C43—21no—
73C23×C4×C43C2311yescharacteristic
74C22×C8×C43—21no—
75C2×C4⋊C4×C43D412yes—
76C2×C22⋊C4×C43—21no—
77#103×C43—44no—
78C22⋊C8×C43—21no—
79C22⋊C8×C43—21no—
80#95×C43—21no—
81C24×C43C2×D411yescharacteristic
82C23×D43—21no—
83C2×Q8×C43—24no—
84C2×Q8×C43—24no—
85C2×Q8×C43—22no—
86C2×Q8×C43—22no—
87C2×Q8×C43—44no—
88C2×Q8×C43—42no—
89C2×Q8×C43—42no—
90C2×Q8×C43—44no—
91C2×Q8×C43—44no—
92C2×Q8×C43—44no—
93C2×Q8×C43—41no—
94C2×Q8×C43—41no—
95C22×C4×C43—24no—
96C22×C4×C43—22no—
97C22×C4×C43—22no—
98C22×C4×C43—42no—
99C22×C4×C43—42no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C2×C22⋊D43—41no—
109C2×C22⋊D43—41no—
110C2×C22⋊D43—41no—
111C2×C22⋊D43—41no—
112C2×C22⋊D43—41no—
113C2×C22⋊D43—41no—
114C22×Dic43—24no—
115C22×Dic43—21no—
116C22×Dic43—22no—
117C22×Dic43—21no—
118C22×Dic43—21no—
119C22×Dic43—21no—
120C22×Dic43—21no—
121C22×Dic43—21no—
122C22×Dic43—21no—
123C22×Dic43—21no—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—42no—
127C22×Dic43—42no—
128C22×Dic43—41no—
129C22×Dic43—41no—
130C22×Dic43SD1612yescomplemented
131C2×D172—21no—
132C2×D172—21no—
133C2×D172—42no—
134C2×C8×C43—42no—
135C2×C8×C43—41no—
136C4⋊C4×C43—42no—
137C22⋊C4×C43—41no—
138C22⋊C4×C43—41no—
139#10621884—48no—
140(C2×D43)⋊C4—44no—
141(C2×D43)⋊C4—41no—
142(C2×D43)⋊C4—41no—
143(C2×D43)⋊C4—82no—
144C4⋊Dic43—21no—
145C4⋊Dic43—21no—
146C4⋊Dic43—44no—
147Dic43⋊C4—48no—
148Dic43⋊C4—41no—
149Dic43⋊C4—41no—
150Dic43⋊C4—41no—
151Dic43⋊C4—41no—
152C2×C43⋊C8—22no—
153C2×C43⋊C8—42no—
154C23×C43—22no—
155C23×C43—22no—
156C23×C43#12011yescharacteristic
157C23×C43#12011yescharacteristic
158C23×C43#12111yescharacteristic
159C23×C43C2×SD1611yescharacteristic
160C23×C43#13511yescharacteristic
161C23×C43AGL(1,ℤ/8)11yescharacteristic
162C23×C43#13711yescharacteristic
163C22×D43—41no—
164C22×D43—41no—
165C22×D43—41no—
166C22×D43—42no—
167C22×D43—42no—
168Q8×C43—24no—
169Q8×C43—24no—
170Q8×C43—42no—
171Q8×C43—44no—
172Q8×C43—44no—
173Q8×C43—42no—
174C2×C4×C43—22no—
175C2×C4×C43—22no—
176C2×C4×C43—24no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—42no—
182C2×C4×C43—44no—
183C2×C4×C43—42no—
184C2×C4×C43—44no—
185C2×C4×C43—42no—
186C2×C4×C43—42no—
187C2×C4×C43—42no—
188C2×C4×C43#12011yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43#12111yescharacteristic
191C2×C4×C43#12711yescharacteristic
192C22⋊D43—81no—
193C22⋊D43—81no—
194C22⋊D43—81no—
195C22⋊D43—81no—
196C2×Dic43—24no—
197C2×Dic43—22no—
198C2×Dic43—22no—
199C2×Dic43—22no—
200C2×Dic43—42no—
201C2×Dic43—44no—
202C2×Dic43—44no—
203C2×Dic43—41no—
204C2×Dic43—41no—
205C2×Dic43—42no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—42no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—42no—
214C2×Dic43—81no—
215D172—42no—
216D172—81no—
217C8×C43—81no—
218C43⋊C8—42no—
219#9917—431nomaximal, Sylow
220C22×C43—22no—
221C22×C43—22no—
222C22×C43—22no—
223C22×C43—22no—
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—21no—
227C22×C43—21no—
228C22×C43#39211yescharacteristic
229C22×C43#44811yescharacteristic
230C22×C43#44911yescharacteristic
231C22×C43#45011yescharacteristic
232C22×C43#45211yescharacteristic
233C22×C43#45612yes—
234C22×C43B(4,𝔽2)12yes—
235C22×C43#46511yescharacteristic
236C22×C43#46811yescharacteristic
237C2×D43—82no—
238C2×D43—82no—
239C2×D43—81no—
240C2×D43—81no—
241C2×D43—81no—
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—21no—
246C4×C43—44no—
247C4×C43—82no—
248Dic43—44no—
249Dic43—42no—
250Dic43—81no—
251Dic43—81no—
252C2×#448—431no—
253#2618—431no—
254C2×#395—431no—
255#1787D4311yescharacteristic, complemented
256C2×#327—431no—
257C2×#324—431no—
258#1294—431no—
259C2×C43—21no—
260C2×C43—21no—
261C2×C43—21no—
262C2×C43—21no—
263C2×C43#160312yes—
264C2×C43#160412yes—
265C2×C43#200011yescharacteristic
266C2×C43#200511yescharacteristic
267C2×C43#202111yescharacteristic
268D43—161no—
269C23×Q8C2×D4311yescharacteristic
270C22×SD16—861no—
271C2×#123—861no—
272C2×#121—431no—
273C22×C4⋊C4—431no—
274C22×C4⋊C4—861no—
275#448—862no—
276#448—862no—
277C2×#103—22no—
278C2×#103—861no—
279C2×C22⋊C8—431no—
280C2×C22⋊C8C2×D4311yescharacteristic
281#398—861no—
282#396—862no—
283#395—862no—
284#395—862no—
285#394—861no—
286#386—861no—
287#380C2×D4311yescharacteristic
288C2×#95—431no—
289C2×#95—861no—
290#327—862no—
291#324—862no—
292C43#991711yescharacteristic, complemented, Sylow
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8—44no—
299C22×Q8D17212yes—
300C22×D4—431no—
301C22×D4—861no—
302C23×C4—21no—
303C23×C4—431no—
304C23×C4—431no—
305C23×C4—861no—
306C23×C4C22×D4311yescharacteristic
307C2×SD16—864no—
308C2×SD16—1724no—
309C22×C8—21no—
310C22×C8—861no—
311#123—1722no—
312#123—1722no—
313#121—861no—
314#121—861no—
315#121—861no—
316#121—861no—
317C2×C4⋊C4—431no—
318C2×C4⋊C4—864no—
319C2×C4⋊C4—862no—
320C2×C4⋊C4—861no—
321C2×C4⋊C4—861no—
322C2×C4⋊C4—861no—
323C2×C4⋊C4—861no—
324C2×C4⋊C4—861no—
325C2×C4⋊C4—861no—
326C2×C4⋊C4—1724no—
327C2×C4⋊C4C22⋊D4312yes—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—862no—
330C2×C22⋊C4—862no—
331C2×C22⋊C4—861no—
332#103—44no—
333#103—864no—
334C22⋊C8—21no—
335C22⋊C8—21no—
336C22⋊C8—432no—
337C22⋊C8—861no—
338#95—21no—
339#95—432no—
340#95—864no—
341#95—862no—
342#95—861no—
343C24—861no—
344C24D4×D4311yescharacteristic
345C2×Q8—24no—
346C2×Q8—24no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—44no—
350C2×Q8—42no—
351C2×Q8—42no—
352C2×Q8—44no—
353C2×Q8—44no—
354C2×Q8—44no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×D4—861no—
358C2×D4—861no—
359C2×D4—1722no—
360C2×D4—1721no—
361C2×D4—1721no—
362C2×D4—1721no—
363C2×D4—1721no—
364C2×D4—1721no—
365C2×D4—1721no—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—432no—
374C22×C4—864no—
375C22×C4—861no—
376C22×C4—862no—
377C22×C4—861no—
378C22×C4—861no—
379C22×C4—861no—
380C22×C4—861no—
381C22×C4—861no—
382C22×C4—861no—
383C22×C4—861no—
384C22×C4—861no—
385C22×C4—861no—
386C22×C4—1722no—
387C22×C4—1722no—
388C22×C4—1721no—
389C22×C4—1721no—
390C22×C4C2×D17211yescharacteristic
391C22×C4#1062189811yescharacteristic
392C22×C4D4×D4311yescharacteristic
393C22×C4D4×D4311yescharacteristic
394C22×C4D4×D4311yescharacteristic
395C22×C4C2×C22⋊D4311yescharacteristic
396SD16—1728no—
397C2×C8—42no—
398C2×C8—41no—
399C2×C8—862no—
400C2×C8—1722no—
401C4⋊C4—42no—
402C4⋊C4—861no—
403C4⋊C4—861no—
404C4⋊C4—1728no—
405C4⋊C4—1724no—
406C4⋊C4—1721no—
407C4⋊C4—1721no—
408C4⋊C4—1721no—
409C4⋊C4—1721no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—3442no—
413C22⋊C4—1724no—
414C22⋊C4—1721no—
415C22⋊C4—1721no—
416C23—22no—
417C23—22no—
418C23—1721no—
419C23—1721no—
420C23—1721no—
421C23—1722no—
422C23—1722no—
423C23#1306329311yescharacteristic
424C23#1306329511yescharacteristic
425C23#1306329811yescharacteristic
426C23SD16×D4311yescharacteristic
427C23#1306334811yescharacteristic
428C23#1306335211yescharacteristic
429C23#1306335711yescharacteristic
430Q8—24no—
431Q8—24no—
432Q8—44no—
433Q8—42no—
434Q8—44no—
435Q8—42no—
436D4—3441no—
437D4—3441no—
438D4—3441no—
439D4—3441no—
440D4—3441no—
441D4—1722no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—44no—
451C2×C4—42no—
452C2×C4—44no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—864no—
457C2×C4—862no—
458C2×C4—862no—
459C2×C4—862no—
460C2×C4—3441no—
461C2×C4—1722no—
462C2×C4—1721no—
463C2×C4—1721no—
464C2×C4—1721no—
465C2×C4—1721no—
466C2×C4—1722no—
467C2×C4—1722no—
468C2×C4—1724no—
469C2×C4—1724no—
470C2×C4—1721no—
471C2×C4—1722no—
472C2×C4—1721no—
473C2×C4—1721no—
474C2×C4—1721no—
475C2×C4#1306329511yescharacteristic
476C2×C4#1306329811yescharacteristic
477C2×C4#1306329911yescharacteristic
478C2×C4#1306332111yescharacteristic
479C8—81no—
480C8—1722no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—3441no—
490C22—3442no—
491C22—3442no—
492C22—3441no—
493C22—3441no—
494C22#1458280811yescharacteristic
495C22#1458303911yescharacteristic
496C22#1458304711yescharacteristic
497C22#1458304811yescharacteristic
498C22#1458306011yescharacteristic
499C22#1458308012yes—
500C22#1458308512yes—
501C22#1458313111yescharacteristic
502C22#1458314811yescharacteristic
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—44no—
508C4—82no—
509C4—3441no—
510C4—3441no—
511C4—1724no—
512C4—1722no—
513C2—21no—
514C2—21no—
515C2—21no—
516C2—21no—
517C2—6881no—
518C2#1913355712yes—
519C2#1913356212yes—
520C2#1913559711yescharacteristic
521C2#1913563211yescharacteristic
522C2#1913572111yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1787C2
socleC23×C43#120
prime radicalC2×#13063299C22
hypercenter#1787D43
hypocenterC43#9917
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#14582818C2semidirect
5. C2×#14582624C2semidirect
6. #19132473C2semidirect
7. C43×#1787C2semidirect
130. C22×Dic43SD16semidirect
255. #1787D43semidirect
292. C43#9917semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145830382
#191403402
C2×#145828182
C2×#145826342
C2×#145826242
#191324732
C43×#17872
#991743